Editing Image (mathematics) (section)

===Image of a subset===

Throughout, let <math>f : X \to Y</math> be a function. 
The {{anchor|image of a set}}{{em|image}} under <math>f</math> of a subset <math>A</math> of <math>X</math> is the set of all <math>f(a)</math> for <math>a\in A.</math> It is denoted by <math>f[A],</math> or by <math>f(A)</math> when there is no risk of confusion. Using [[set-builder notation]], this definition can be written as<ref>{{Cite web|date=2019-11-05| title=5.4: Onto Functions and Images/Preimages of Sets| url=https://math.libretexts.org/Courses/Monroe_Community_College/MTH_220_Discrete_Math/5%3A_Functions/5.4%3A_Onto_Functions_and_Images%2F%2FPreimages_of_Sets| access-date=2020-08-28| website=Mathematics LibreTexts| language=en}}</ref><ref>{{cite book| author=Paul R. Halmos| title=Naive Set Theory| location=Princeton| publisher=Nostrand| year=1968 }} Here: Sect.8</ref>
<math display=block>f[A] = \{f(a) : a \in A\}.</math>

This induces a function <math>f[\,\cdot\,] : \mathcal P(X) \to \mathcal P(Y),</math> where <math>\mathcal P(S)</math> denotes the [[power set]] of a set <math>S;</math> that is the set of all [[subset]]s of <math>S.</math> See {{Section link||Notation}} below for more.